We show experimentally, and explain theoretically, what velocity is needed to break an elongated droplet entering a microfluidic T-junction. Our experiments on short droplets confirm previous experimental and theoretical work that shows that the critical velocity for breakup scales with the inverse of the length of the droplet raised to the fifth power. For long elongated droplets that have a length about thrice the channel width, we reveal a drastically different scaling. Taking into account that a long droplet remains squeezed between the channel walls when it enters a T-junction, such that the gutters in the corners of the channel are the main route for the continuous phase to flow around the droplet, we developed a model that explains that the critical velocity for breakup is inversely proportional to the droplet length. This model for the transition between breaking and nonbreaking droplets is in excellent agreement with our experiments.

The segmented flow of droplets and bubbles in channels of micrometer size occurs in numerous (bio) chemistry applications and an important question is whether (and how) a droplet (or bubble) entering a branching micro-channel breaks. In this work, we address this question using the T-junction as a paradigm. We performed experiments at low capillary numbers, with droplets of different sizes entering a T-junction. Our experiments show (i) the existence of stable non-breaking droplets (trapped inside the T-junction) at sufficiently low speeds, and (ii) that the critical speed at which the droplets break differs considerably from the scaling rules proposed in the literature. We developed a semi-empirical model that takes into account the 3D nature of the problem (with the flow around the droplet, through the gutters), which is not done in the scaling models proposed in the literature. Our model agrees well with the experimentally observed scaling and explains the change of scaling at low capillary numbers.